Pattern formation

Specifically, we are interested in modelling of chemical and mechanical aspects of the generation of pattern and form in embryology and development. Applications include skeletal patterning in the vertebrate limb, primitive streak formation, somitogenesis, skin organ formation (feather bud formation, tooth initiation), tissue movement during invagination processes, tissue-tissue interactions in, for example, determining lung morphology, cell aggregation in Dictyostelium, patterning generation in Hydra.

Please contact Professor Philip K. Maini or Dr Ruth E. Baker for more details.

Theoretical studies on pattern formation 

We use systems of partial differential equations to try and understand how the non-linear interactions between patterning elements combine to give rise to spatio-temporal patterning. In particular, we are interested in Turing patterns, mechano-chemical and chemotaxis models. Current work is concerned with the effect of delays upon pattern formation and the role of stochasticity.

Comparison of pattern formation in the Schnakenberg model using both continuous and discrete approaches. 

Key references in this area

    • S. Seirin Lee and E. A. Gaffney (2010). Aberrant behaviours of reaction diffusion self-organisation models on growing domains in the presence of gene expression time delays. Bull. Math. Biol. 72:2161-2179. (eprints)
    • S. Seirin Lee, E. A. Gaffney and N. A. M. Monk (2010). The influence of gene expression time delays on Gierer-Meinhardt pattern formation systems. Bull. Math. Biol. 72:2139-2160. (eprints)
    • T. E. Woolley, R. E. Baker, P. K. Maini, J. L. Aragon and R. Barrio (2010). Analysis of stationary droplets in a generic Turing reaction-diffusion system. Phys. Rev. E. 82:051929. (eprints
    • T. E. Woolley, R. E. Baker, E. A. Gaffney and P. K. Maini (2011). Power spectra methods for a stochastic description of diffusion on deterministically growing domains Phys. Rev. E. 84(2):021915 (eprints
    • T. E. Woolley, R. E. Baker, E. A. Gaffney and P. K. Maini (2011). The influence of stochastic domain growth on pattern nucleation for diffusive systems with internal noise. Phys. Rev. E. 84(4):041095. (eprints
    • T. E. Woolley, R. E. Baker, E. A. Gaffney and P. K. Maini (2011). Stochastic reaction and diffusion on growing domains: Understanding the breakdown of robust pattern formation. Phys. Rev. E.84(4):046216. (eprints
    • V. Klika, R. E. Baker, D. J. Headon and E. A. Gaffney (2012). The influence of receptor-mediated interactions on reaction-diffusion mechanisms of cellular self-organisation. Bull. Math. Biol. 74(4):935–957. (eprints)


    Somitogenesis, the sequential production of a periodic pattern along the head-tail (HT) axis of vertebrate embryos, is one of the most obvious examples of the patterning processes that take place during embryogenesis. Segmentation is visualised by the sequential formation of bilateral blocks of cells, the somites, from the rostral extremity of the presomitic mesoderm (PSM). Genetic or environmental factors can disturb somitogenesis, and there are many recognized clinical conditions that can occur as a result. In humans, disturbance of the somitogenic processes can cause abnormal segmentation of the vertebral column, leading to defects such as rib fusions and wedge and butterfly vertebrae. Studying the developmental mechanisms in vertebral patterning will aid in the identification of protective or potentially disruptive factors for normal somitogenesis, and could lead towards treatments for the prevention of vertebral patterning disorders.

    We are interested in modelling somitogenesis from a number of viewpoints. Firstly, we use a reaction-diffusion model with bistable kinetics to understand how a travelling wavefront of determination interacts with a "segmentation clock" in order to gate cells into presumptive somites. More recently, we have been developing coupled oscillator models to explore in more depth the mechanisms underlying the clock. 


    Somites in the early chick embryo.
    Figure courtesy of Paul Kulesa, Stowers Institute for Medical Research. 

    Key references in this area

    • P. J. Murray, P. K. Maini and R. E. Baker (2011). The clock and wavefront model revisited. J. Theor. Biol. 283:227-238. (eprints)
    • R. E. Baker, S. Schnell and P. K. Maini (2006). A clock and wavefront mechanism for somite formation. Dev. Biol. 293:116-126. (eprints)
    • R. E. Baker, S. Schnell and P. K. Maini (2006). A mathematical investigation of a new model for somitogenesis. J. Math. Biol. 52:458-482. (eprints)

    Skin patterning

    In collaboration with Professor Cheng-Ming Chuong (University of Southern California) we are interested in understanding the mechanisms behind skin patterning, for example, feather and scale formation, and hair follicle cycling. Feathers, hairs and scales all arise via interactions between the dermis and epidermis during early development which lead to cell condensations, the early skin integuments. We use a range of approaches to investigate the nature of possible patterns including reaction-diffusion and cell-chemotaxis models, mechano-chemical models and cellular Potts models. Patterns in hair follicle cycling are seen in several species throughout the adult life: regions of the skin display coordinated follicle cycling that may be observed as pigmentation patterns on the skin. We use cellular automata models to investigate the nature of the patterns formed and how different types of patterns may be observed in gene mutants.

    Key references in this area

    • C.-M. Lin, T. X. Jiang, R. E. Baker, P. K. Maini, R. B. Widelitz and C.-M. Chuong (2009). Spots and stripes: Pleomorphic patterning of stem cells via p-ERK-dependent cell chemotaxis shown by feather morphogenesis and mathematical simulation. Dev. Biol. 334:369–382. (eprints)
    • M. V. Plikus, D. De La Cruz, J. Mayer, R. E. Baker, R. Maxon, P. K. Maini and C.-M. Chuong (2008). Cyclic dermal BMP signalling regulates stem cell activation during hair regeneration. Nature 451:340-344. (eprints)


    We have also addressed issues such as patterning in mouse tooth development and Drosophila gradient formation.

    Key references in this area

    • M. V. Plikus, R. E. Baker, C. C. Chen, C. Fare, D. de la Cruz, T. Andl, P. K. Maini, S. E. Miller, R. Widelitz and C. M. Chuong (2011). Self-organizing and stochastic behaviors during the regeneration of hair stem cells. Science 332:586-589. (eprints)
    • S. W. Cho, S. W. Kwak, T. E. Woolley, M. J. Lee, E. J. Kim, R. E. Baker, H. J. Kim, J. S. Shin, C. Tickle, P. K. Maini and H. S. Jung (2011). Interactions between Shh, Sostdc1 and Wnt signaling and a new feedback loop for spatial patterning of the teeth. Development 138:1807-1816. (eprints)